{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Naive Bayes and Bayes Classifiers\n",
    "\n",
    "author: Jacob Schreiber <br>\n",
    "contact: jmschreiber91@gmail.com\n",
    "\n",
    "Bayes classifiers are some of the simplest machine learning models that exist, due to their intuitive probabilistic interpretation and simple fitting step. Each class is modeled as a probability distribution, and the data is interpreted as samples drawn from these underlying distributions. Fitting the model to data is as simple as calculating maximum likelihood parameters for the data that falls under each class, and making predictions is as simple as using Bayes' rule to determine which class is most likely given the distributions. Bayes' Rule is the following: \n",
    "\n",
    "\\begin{equation}\n",
    "P(M|D) = \\frac{P(D|M)P(M)}{P(D)}\n",
    "\\end{equation}\n",
    "\n",
    "where M stands for the model and D stands for the data. $P(M)$ is known as the <i>prior</i>, because it is the probability that a sample is of a certain class before you even know what the sample is. This is generally just the frequency of each class. Intuitively, it makes sense that you would want to model this, because if one class occurs 10x more than another class, it is more likely that a given sample will belong to that distribution. $P(D|M)$ is the likelihood, or the probability, of the data under a given model. Lastly, $P(M|D)$ is the posterior, which is the probability of each component of the model, or class, being the component which generated the data. It is called the posterior because the prior corresponds to probabilities before seeing data, and the posterior corresponds to probabilities after observing the data. In cases where the prior is uniform, the posterior is just equal to the normalized likelihoods. This equation forms the basis of most probabilistic modeling, with interesting priors allowing the user to inject sophisticated expert knowledge into the problem directly.\n",
    "\n",
    "pomegranate implements two distinct models of this format with the simpler being the naive Bayes classifier. The naive Bayes classifier assumes that each feature is independent from each other feature, and so breaks down $P(D|M)$ to be $\\prod\\limits_{i=1}^{d} P(D_{i}|M_{i})$ where $i$ is a specific feature in a data set that has $d$ features in it. This typically means faster calculations because covariance across features doesn't need to be considered, but it also is a natural way to model each feature as a different distribution because it ignores the complexities of modeling the covariance between, say, an exponential distribution and a normal distribution.\n",
    "\n",
    "The more general model is the Bayes classifier which does not assume that each feature is independent of the others. This allows you to plug in anything for the likelihood function, whether it be a multivariate Gaussian distribution or a whole other compositional model. For instance, one could create a classifier whose components are each large mixture models. This enables much more complex models to be learned within the simple framework of Bayes' rule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fri Jan 10 2020 \n",
      "\n",
      "numpy 1.18.1\n",
      "scipy 1.4.1\n",
      "pomegranate 0.12.0\n",
      "\n",
      "compiler   : Clang 10.0.0 (clang-1000.11.45.5)\n",
      "system     : Darwin\n",
      "release    : 17.7.0\n",
      "machine    : x86_64\n",
      "processor  : i386\n",
      "CPU cores  : 4\n",
      "interpreter: 64bit\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; seaborn.set_style('whitegrid')\n",
    "import numpy\n",
    "\n",
    "from pomegranate import *\n",
    "\n",
    "numpy.random.seed(0)\n",
    "numpy.set_printoptions(suppress=True)\n",
    "\n",
    "%load_ext watermark\n",
    "%watermark -m -n -p numpy,scipy,pomegranate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple Gaussian Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = numpy.concatenate((numpy.random.normal(3, 1, 200), numpy.random.normal(10, 2, 1000)))\n",
    "y = numpy.concatenate((numpy.zeros(200), numpy.ones(1000)))\n",
    "\n",
    "x1 = X[:200]\n",
    "x2 = X[200:]\n",
    "\n",
    "plt.figure(figsize=(16, 5))\n",
    "plt.hist(x1, bins=25, color='m', edgecolor='m', label=\"Class A\")\n",
    "plt.hist(x2, bins=25, color='c', edgecolor='c', label=\"Class B\")\n",
    "plt.xlabel(\"Value\", fontsize=14)\n",
    "plt.ylabel(\"Count\", fontsize=14)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data seems like it comes from two normal distributions, with the cyan class being more prevalent than the magenta class. A natural way to model this data would be to create a normal distribution for the cyan data, and another for the magenta distribution.\n",
    "\n",
    "Let's take a look at doing that. All we need to do is use the `from_samples` class method of the `NormalDistribution` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d1 = NormalDistribution.from_samples(x1)\n",
    "d2 = NormalDistribution.from_samples(x2)\n",
    "idxs = numpy.arange(0, 15, 0.1)\n",
    "\n",
    "p1 = list(map(d1.probability, idxs))\n",
    "p2 = list(map(d2.probability, idxs))\n",
    "\n",
    "plt.figure(figsize=(16, 5))\n",
    "plt.plot(idxs, p1, color='m'); plt.fill_between(idxs, 0, p1, facecolor='m', alpha=0.2)\n",
    "plt.plot(idxs, p2, color='c'); plt.fill_between(idxs, 0, p2, facecolor='c', alpha=0.2)\n",
    "plt.xlabel(\"Value\", fontsize=14)\n",
    "plt.ylabel(\"Probability\", fontsize=14)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like some aspects of the data are captured well by doing things this way-- specifically the mean and variance of the normal distributions. This allows us to easily calculate $P(D|M)$ as the probability of a sample under either the cyan or magenta distributions using the normal (or Gaussian) probability density equation:\n",
    "\n",
    "\\begin{align}\n",
    "P(D|M) &= P(x|\\mu, \\sigma) \\\\\n",
    "       &= \\frac{1}{\\sqrt{2\\pi\\sigma^{2}}} exp \\left(-\\frac{(x-u)^{2}}{2\\sigma^{2}} \\right) \n",
    "\\end{align}\n",
    "\n",
    "However, if we look at the original data, we see that the cyan distributions is both much wider than the purple distribution and much taller, as there were more samples from that class in general. If we reduce that data down to these two distributions, we lose the class imbalance. We want our prior to model this class imbalance, with the reasoning being that if we randomly draw a sample from the samples observed thus far, it is far more likely to be a cyan than a magenta sample. Let's take a look at this class imbalance exactly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "magenta_prior = 1. * len(x1) / len(X)\n",
    "cyan_prior = 1. * len(x2) / len(X)\n",
    "\n",
    "plt.figure(figsize=(4, 6))\n",
    "plt.title(\"Prior Probabilities P(M)\", fontsize=14)\n",
    "plt.bar(0, magenta_prior, facecolor='m', edgecolor='m')\n",
    "plt.bar(1, cyan_prior, facecolor='c', edgecolor='c')\n",
    "plt.xticks([0, 1], ['P(Magenta)', 'P(Cyan)'], fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prior $P(M)$ is a vector of probabilities over the classes that the model can predict, also known as components. In this case, if we draw a sample randomly from the data that we have, there is a ~83% chance that it will come from the cyan class and a ~17% chance that it will come from the magenta class.\n",
    "\n",
    "Let's multiply the probability densities we got before by this imbalance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d1 = NormalDistribution.from_samples(x1)\n",
    "d2 = NormalDistribution.from_samples(x2)\n",
    "idxs = numpy.arange(0, 15, 0.1)\n",
    "\n",
    "p_magenta = numpy.array(list(map(d1.probability, idxs))) * magenta_prior\n",
    "p_cyan = numpy.array(list(map(d2.probability, idxs))) * cyan_prior\n",
    "\n",
    "plt.figure(figsize=(16, 5))\n",
    "plt.plot(idxs, p_magenta, color='m'); plt.fill_between(idxs, 0, p_magenta, facecolor='m', alpha=0.2)\n",
    "plt.plot(idxs, p_cyan, color='c'); plt.fill_between(idxs, 0, p_cyan, facecolor='c', alpha=0.2)\n",
    "plt.xlabel(\"Value\", fontsize=14)\n",
    "plt.ylabel(\"P(M)P(D|M)\", fontsize=14)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks a lot more faithful to the original data, and actually corresponds to $P(M)P(D|M)$, the prior multiplied by the likelihood. However, these aren't actually probability distributions anymore, as they no longer integrate to 1. This is why the $P(M)P(D|M)$ term has to be normalized by the $P(D)$ term in Bayes' rule in order to get a probability distribution over the components. However, $P(D)$ is difficult to determine exactly-- what is the probability of the data? Well, we can sum over the classes to get that value, since $P(D) = \\sum_{i=1}^{c} P(D|M)P(M)$ for a problem with c classes. This translates into $P(D) = P(M=Cyan)P(D|M=Cyan) + P(M=Magenta)P(D|M=Magenta)$ for this specific problem, and those values can just be pulled from the unnormalized plots above.\n",
    "\n",
    "This gives us the full Bayes' rule, with the posterior $P(M|D)$ being the proportion of density of the above plot coming from each of the two distributions at any point on the line. Let's take a look at the posterior probabilities of the two classes on the same line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "magenta_posterior = p_magenta / (p_magenta + p_cyan)\n",
    "cyan_posterior = p_cyan / (p_magenta + p_cyan)\n",
    "\n",
    "plt.figure(figsize=(16, 5))\n",
    "plt.subplot(211)\n",
    "plt.plot(idxs, p_magenta, color='m'); plt.fill_between(idxs, 0, p_magenta, facecolor='m', alpha=0.2)\n",
    "plt.plot(idxs, p_cyan, color='c'); plt.fill_between(idxs, 0, p_cyan, facecolor='c', alpha=0.2)\n",
    "plt.xlabel(\"Value\", fontsize=14)\n",
    "plt.ylabel(\"P(M)P(D|M)\", fontsize=14)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "\n",
    "plt.subplot(212)\n",
    "plt.plot(idxs, magenta_posterior, color='m')\n",
    "plt.plot(idxs, cyan_posterior, color='c')\n",
    "plt.xlabel(\"Value\", fontsize=14)\n",
    "plt.ylabel(\"P(M|D)\", fontsize=14)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The top plot shows the same densities as before, while the bottom plot shows the proportion of the density belonging to either class at that point. This proportion is known as the posterior $P(M|D)$, and can be interpreted as the probability of that point belonging to each class. This is one of the native benefits of probabilistic models, that instead of providing a hard class label for each sample, they can provide a soft label in the form of the probability of belonging to each class.\n",
    "\n",
    "We can implement all of this simply in pomegranate using the `NaiveBayes` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idxs = idxs.reshape(idxs.shape[0], 1)\n",
    "X = X.reshape(X.shape[0], 1)\n",
    "\n",
    "model = NaiveBayes.from_samples(NormalDistribution, X, y)\n",
    "posteriors = model.predict_proba(idxs)\n",
    "\n",
    "plt.figure(figsize=(14, 4))\n",
    "plt.plot(idxs, posteriors[:,0], color='m')\n",
    "plt.plot(idxs, posteriors[:,1], color='c')\n",
    "plt.xlabel(\"Value\", fontsize=14)\n",
    "plt.ylabel(\"P(M|D)\", fontsize=14)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like we're getting the same plots for the posteriors just through fitting the naive Bayes model directly to data. The predictions made will come directly from the posteriors in this plot, with cyan predictions happening whenever the cyan posterior is greater than the magenta posterior, and vice-versa."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Naive Bayes\n",
    "\n",
    "In the univariate setting, naive Bayes is identical to a general Bayes classifier. The divergence occurs in the multivariate setting, the naive Bayes model assumes independence of all features, while a Bayes classifier is more general and can support more complicated interactions or covariances between features. Let's take a look at what this means in terms of Bayes' rule. \n",
    "\n",
    "\\begin{align}\n",
    "P(M|D) &= \\frac{P(M)P(D|M)}{P(D)} \\\\\n",
    "       &= \\frac{P(M)\\prod_{i=1}^{d}P(D_{i}|M_{i})}{P(D)}\n",
    "\\end{align}\n",
    "\n",
    "This looks fairly simple to compute, as we just need to pass each dimension into the appropriate distribution and then multiply the returned probabilities together. This simplicity is one of the reasons why naive Bayes is so widely used. Let's look closer at using this in pomegranate, starting off by generating two blobs of data that overlap a bit and inspecting them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = numpy.concatenate([numpy.random.normal(3, 2, size=(150, 2)), numpy.random.normal(7, 1, size=(250, 2))])\n",
    "y = numpy.concatenate([numpy.zeros(150), numpy.ones(250)])\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='c')\n",
    "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='m')\n",
    "plt.xlim(-2, 10)\n",
    "plt.ylim(-4, 12)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's fit our naive Bayes model to this data using pomegranate. We can use the `from_samples` class method, pass in the distribution that we want to model each dimension, and then the data. We choose to use `NormalDistribution` in this particular case, but any supported distribution would work equally well, such as `BernoulliDistribution` or `ExponentialDistribution`. To ensure we get the correct decision boundary, let's also plot the boundary recovered by sklearn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "\n",
    "model = NaiveBayes.from_samples(NormalDistribution, X, y)\n",
    "clf = GaussianNB().fit(X, y)\n",
    "\n",
    "xx, yy = numpy.meshgrid(numpy.arange(-2, 10, 0.02), numpy.arange(-4, 12, 0.02))\n",
    "Z1 = model.predict(numpy.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n",
    "Z2 = clf.predict(numpy.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n",
    "\n",
    "plt.figure(figsize=(16, 8))\n",
    "plt.subplot(121)\n",
    "plt.title(\"pomegranate naive Bayes\", fontsize=16)\n",
    "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='c')\n",
    "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='m')\n",
    "plt.contour(xx, yy, Z1, cmap='Blues')\n",
    "plt.xlim(-2, 10)\n",
    "plt.ylim(-4, 12)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.title(\"sklearn naive Bayes\", fontsize=16)\n",
    "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='c')\n",
    "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='m')\n",
    "plt.contour(xx, yy, Z2, cmap='Blues')\n",
    "plt.xlim(-2, 10)\n",
    "plt.ylim(-4, 12)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Drawing the decision boundary helps to verify that we've produced a good result by cleanly splitting the two blobs from each other.\n",
    "\n",
    "Bayes' rule provides a great deal of flexibility in terms of what the actually likelihood functions are. For example, when considering a multivariate distribution, there is no need for each dimension to be modeled by the same distribution. In fact, each dimension can be modeled by a different distribution, as long as we can multiply the $P(D|M)$ terms together. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classifying Signal with Different Distributions on Different Features\n",
    "\n",
    "Let's consider the example of some noisy signals that have been segmented. We know that they come from two underlying phenomena, the cyan phenomena and the magenta phenomena, and want to classify future segments. To do this, we have three features-- the mean signal of the segment, the standard deviation, and the duration.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_signal(X, n):\n",
    "    plt.figure(figsize=(16, 6))\n",
    "    t_current = 0\n",
    "    for i in range(n):\n",
    "        mu, std, t = X[i]\n",
    "        chunk = numpy.random.normal(mu, std, int(t))\n",
    "        plt.plot(numpy.arange(t_current, t_current+t), chunk, c='cm'[i % 2])\n",
    "        t_current += t\n",
    "    \n",
    "    plt.xticks(fontsize=14)\n",
    "    plt.yticks(fontsize=14)\n",
    "    plt.xlabel(\"Time (s)\", fontsize=14)\n",
    "    plt.ylabel(\"Signal\", fontsize=14)\n",
    "    plt.ylim(20, 40)\n",
    "    plt.show()\n",
    "\n",
    "def create_signal(n):\n",
    "    X, y = [], []\n",
    "    for i in range(n):\n",
    "        mu = numpy.random.normal(30.0, 0.4)\n",
    "        std = numpy.random.lognormal(-0.1, 0.4)\n",
    "        t = int(numpy.random.exponential(50)) + 1\n",
    "        X.append([mu, std, int(t)])\n",
    "        y.append(0)\n",
    "\n",
    "        mu = numpy.random.normal(30.5, 0.8)\n",
    "        std = numpy.random.lognormal(-0.3, 0.6)\n",
    "        t = int(numpy.random.exponential(200)) + 1\n",
    "        X.append([mu, std, int(t)])\n",
    "        y.append(1)\n",
    "    \n",
    "    return numpy.array(X), numpy.array(y)\n",
    "\n",
    "X_train, y_train = create_signal(1000)\n",
    "X_test, y_test = create_signal(250)\n",
    "plot_signal(X_train, 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can start by modeling each variable as Gaussians, like before, and see what accuracy we get."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian Naive Bayes:  0.794\n",
      "sklearn Gaussian Naive Bayes:  0.794\n"
     ]
    }
   ],
   "source": [
    "model = NaiveBayes.from_samples(NormalDistribution, X_train, y_train)\n",
    "print(\"Gaussian Naive Bayes: \", (model.predict(X_test) == y_test).mean())\n",
    "\n",
    "clf = GaussianNB().fit(X_train, y_train)\n",
    "print(\"sklearn Gaussian Naive Bayes: \", (clf.predict(X_test) == y_test).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get identical values for sklearn and for pomegranate, which is good. However, let's take a look at the data itself to see whether a Gaussian distribution is the appropriate distribution for the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14, 4))\n",
    "plt.subplot(131)\n",
    "plt.title(\"Mean\")\n",
    "plt.hist(X_train[y_train == 0, 0], color='c', alpha=0.5, bins=25)\n",
    "plt.hist(X_train[y_train == 1, 0], color='m', alpha=0.5, bins=25)\n",
    "\n",
    "plt.subplot(132)\n",
    "plt.title(\"Standard Deviation\")\n",
    "plt.hist(X_train[y_train == 0, 1], color='c', alpha=0.5, bins=25)\n",
    "plt.hist(X_train[y_train == 1, 1], color='m', alpha=0.5, bins=25)\n",
    "\n",
    "plt.subplot(133)\n",
    "plt.title(\"Duration\")\n",
    "plt.hist(X_train[y_train == 0, 2], color='c', alpha=0.5, bins=25)\n",
    "plt.hist(X_train[y_train == 1, 2], color='m', alpha=0.5, bins=25)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, unsurprisingly (since you can see that I used non-Gaussian distributions to generate the data originally), it looks like only the mean follows a normal distribution, whereas the standard deviation seems to follow either a gamma or a log-normal distribution. We can take advantage of that by explicitly using these distributions instead of approximating them as normal distributions. pomegranate is flexible enough to allow for this, whereas sklearn currently is not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian Naive Bayes:  0.794\n",
      "sklearn Gaussian Naive Bayes:  0.794\n",
      "Heterogeneous Naive Bayes:  0.822\n"
     ]
    }
   ],
   "source": [
    "model = NaiveBayes.from_samples(NormalDistribution, X_train, y_train)\n",
    "print(\"Gaussian Naive Bayes: \", (model.predict(X_test) == y_test).mean())\n",
    "\n",
    "clf = GaussianNB().fit(X_train, y_train)\n",
    "print(\"sklearn Gaussian Naive Bayes: \", (clf.predict(X_test) == y_test).mean())\n",
    "\n",
    "model = NaiveBayes.from_samples([NormalDistribution, LogNormalDistribution, ExponentialDistribution], X_train, y_train)\n",
    "print(\"Heterogeneous Naive Bayes: \", (model.predict(X_test) == y_test).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like we're able to get a small improvement in accuracy just by using appropriate distributions for the features, without any type of data transformation or filtering. This certainly seems worthwhile if you can determine what the appropriate underlying distribution is.\n",
    "\n",
    "Next, there's obviously the issue of speed. Let's compare the speed of the pomegranate implementation and the sklearn implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "710 µs ± 15.8 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
      "547 µs ± 3.91 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
      "568 µs ± 5.77 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit GaussianNB().fit(X_train, y_train)\n",
    "%timeit NaiveBayes.from_samples(NormalDistribution, X_train, y_train)\n",
    "%timeit NaiveBayes.from_samples([NormalDistribution, LogNormalDistribution, ExponentialDistribution], X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks as if on this small dataset they're all taking approximately the same time. This is pretty much expected, as the fitting step is fairly simple and both implementations use C-level numerics for the calculations. We can give a more thorough treatment of the speed comparison on larger datasets. Let's look at the average time it takes to fit a model to data of increasing dimensionality across 25 runs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "pom_time, skl_time = [], []\n",
    "\n",
    "n1, n2 = 15000, 60000,\n",
    "for d in range(1, 101, 5): \n",
    "    X = numpy.concatenate([numpy.random.normal(3, 2, size=(n1, d)), numpy.random.normal(7, 1, size=(n2, d))])\n",
    "    y = numpy.concatenate([numpy.zeros(n1), numpy.ones(n2)])\n",
    "\n",
    "    tic = time.time()\n",
    "    for i in range(25):\n",
    "        GaussianNB().fit(X, y)\n",
    "    skl_time.append((time.time() - tic) / 25)\n",
    "    \n",
    "    tic = time.time()\n",
    "    for i in range(25):\n",
    "        NaiveBayes.from_samples(NormalDistribution, X, y)\n",
    "    pom_time.append((time.time() - tic) / 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14, 6))\n",
    "plt.plot(range(1, 101, 5), pom_time, color='c', label=\"pomegranate\")\n",
    "plt.plot(range(1, 101, 5), skl_time, color='m', label=\"sklearn\")\n",
    "plt.xticks(fontsize=14)\n",
    "plt.xlabel(\"Number of Dimensions\", fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.ylabel(\"Time (s)\")\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears as if the two implementations are basically the same speed. This is unsurprising given the simplicity of the calculations, and as mentioned before, the low level implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multivariate Gaussian Bayes Classifiers\n",
    "\n",
    "The natural generalization of the naive Bayes classifier is to allow any multivariate function take the place of $P(D|M)$ instead of it being the product of several univariate probability distributions. One immediate difference is that now instead of creating a Gaussian model with effectively a diagonal covariance matrix, you can now create one with a full covariance matrix. Let's see an example of that at work."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tilt_a = [[-2, 0.5], [5, 2]]\n",
    "tilt_b = [[-1, 1.5], [3, 3]]\n",
    "\n",
    "X = numpy.concatenate((numpy.random.normal(4, 1, size=(250, 2)).dot(tilt_a), numpy.random.normal(3, 1, size=(800, 2)).dot(tilt_b)))\n",
    "y = numpy.concatenate((numpy.zeros(250), numpy.ones(800)))\n",
    "\n",
    "model_a = NaiveBayes.from_samples(NormalDistribution, X, y)\n",
    "model_b = BayesClassifier.from_samples(MultivariateGaussianDistribution, X, y)\n",
    "\n",
    "xx, yy = numpy.meshgrid(numpy.arange(-5, 30, 0.02), numpy.arange(0, 25, 0.02))\n",
    "Z1 = model_a.predict(numpy.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n",
    "Z2 = model_b.predict(numpy.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n",
    "\n",
    "plt.figure(figsize=(18, 8))\n",
    "plt.subplot(121)\n",
    "plt.contour(xx, yy, Z1, cmap='Blues')\n",
    "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='c', alpha=0.3)\n",
    "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='m', alpha=0.3)\n",
    "plt.xlim(-5, 30)\n",
    "plt.ylim(0, 25)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.contour(xx, yy, Z2, cmap='Blues')\n",
    "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='c', alpha=0.3)\n",
    "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='m', alpha=0.3)\n",
    "plt.xlim(-5, 30)\n",
    "plt.ylim(0, 25)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like we are able to get a better boundary between the two blobs of data. The primary for this is because the data don't form spherical clusters, like you assume when you force a diagonal covariance matrix, but are tilted ellipsoids, that can be better modeled by a full covariance matrix. We can quantify this quickly by looking at performance on the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "naive training accuracy: 0.9219\n",
      "bayes classifier training accuracy: 0.9695\n"
     ]
    }
   ],
   "source": [
    "print(\"naive training accuracy: {:4.4}\".format((model_a.predict(X) == y).mean()))\n",
    "print(\"bayes classifier training accuracy: {:4.4}\".format((model_b.predict(X) == y).mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like there is a significant boost. Naturally you'd want to evaluate the performance of the model on separate validation data, but for the purposes of demonstrating the effect of a full covariance matrix this should be sufficient."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Mixture Model Bayes Classifier\n",
    "\n",
    "While using a full covariance matrix is certainly more complicated than using only the diagonal, there is no reason that the $P(D|M)$ has to even be a single simple distribution versus a full probabilistic model. After all, all probabilistic models, including general mixtures, hidden Markov models, and Bayesian networks, can calculate $P(D|M)$. Let's take a look at an example of using a mixture model instead of a single gaussian distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = numpy.empty(shape=(0, 2))\n",
    "X = numpy.concatenate((X, numpy.random.normal(4, 1, size=(200, 2)).dot([[-2, 0.5], [2, 0.5]])))\n",
    "X = numpy.concatenate((X, numpy.random.normal(3, 1, size=(350, 2)).dot([[-1, 2], [1, 0.8]])))\n",
    "X = numpy.concatenate((X, numpy.random.normal(7, 1, size=(700, 2)).dot([[-0.75, 0.8], [0.9, 1.5]])))\n",
    "X = numpy.concatenate((X, numpy.random.normal(6, 1, size=(120, 2)).dot([[-1.5, 1.2], [0.6, 1.2]])))\n",
    "y = numpy.concatenate((numpy.zeros(550), numpy.ones(820)))\n",
    "\n",
    "model_a = BayesClassifier.from_samples(MultivariateGaussianDistribution, X, y)\n",
    "\n",
    "gmm_a = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, 2, X[y == 0])\n",
    "gmm_b = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, 2, X[y == 1])\n",
    "model_b = BayesClassifier([gmm_a, gmm_b], weights=numpy.array([1-y.mean(), y.mean()]))\n",
    "\n",
    "xx, yy = numpy.meshgrid(numpy.arange(-10, 10, 0.02), numpy.arange(0, 25, 0.02))\n",
    "Z1 = model_a.predict(numpy.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n",
    "Z2 = model_b.predict(numpy.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n",
    "centroids1 = numpy.array([distribution.mu for distribution in model_a.distributions])\n",
    "centroids2 = numpy.concatenate([[distribution.mu for distribution in component.distributions] for component in model_b.distributions])\n",
    "\n",
    "plt.figure(figsize=(18, 8))\n",
    "plt.subplot(121)\n",
    "plt.contour(xx, yy, Z1, cmap='Blues')\n",
    "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='c', alpha=0.3)\n",
    "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='m', alpha=0.3)\n",
    "plt.scatter(centroids1[:,0], centroids1[:,1], color='k', s=100)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.contour(xx, yy, Z2, cmap='Blues')\n",
    "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='c', alpha=0.3)\n",
    "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='m', alpha=0.3)\n",
    "plt.scatter(centroids2[:,0], centroids2[:,1], color='k', s=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Frequently in the real world you will end up with data that looks like the ones in the above plots, not neatly falling into any single simple distribution. Using a mixture here allowed us to model the various components separately and get a more sophisticated decision boundary that doesn't seem to be extremely overfit.\n",
    "\n",
    "If one wanted to use hidden Markov models to model sequences, all that needs to change is passing in `HiddenMarkovModel` objects instead of `GeneralMixtureModel` ones. Likewise, Bayesian networks are similarly supported and can be passed in just as easily. In fact, the most stacking one could reasonably do is to create a Bayes classifier that distinguishes mixtures of hidden Markov models with mixture emissions (GMM-HMM-GMMs) from each other!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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